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pro vyhledávání: '"Chatterjee, Tapas"'
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $\theta$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $\theta$ over the rationals. Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we chara
Externí odkaz:
http://arxiv.org/abs/2408.14524
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $f(x)=x^{n}+ax^{3}+bx+c$ be the minimal polynomial of an algebraic integer $\theta$ over the rationals with certain conditions on $a,~b,~c,$ and $n.$ Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K
Externí odkaz:
http://arxiv.org/abs/2408.14117
Does $20$ have a friend? Or is it a solitary number? A folklore conjecture asserts that $20$ has no friends i.e. it is a solitary number. In this article, we prove that, a friend $N$ of $20$ is of the form $N=2\cdot5^{2a}m^2$ and it has atleast six d
Externí odkaz:
http://arxiv.org/abs/2409.04451
Autor:
Chatterjee, Tapas, Dhillon, Sonika
In this paper we address the question of non-vanishing of $L'(0,f)$ where $f$ is an algebraic valued periodic function. In 2011, Gun, Murty and Rath studied the nature of special values of the derivatives of even Dirichlet-type functions and proved t
Externí odkaz:
http://arxiv.org/abs/2408.13737
Autor:
Chatterjee, Tapas, Laha, Ayantika
In $2014$, Gupta and Ray proved that the circulant involutory matrices over the finite field $\mathbb{F}_{2^m}$ can not be maximum distance separable (MDS). This non-existence also extends to circulant orthogonal matrices of order $2^d \times 2^d$ ov
Externí odkaz:
http://arxiv.org/abs/2406.16973
Autor:
Chatterjee, Tapas, Laha, Ayantika
Circulant Maximum Distance Separable (MDS) matrices have gained significant importance due to their applications in the diffusion layer of the AES block cipher. In $2013$, Gupta and Ray established that circulant involutory matrices of order greater
Externí odkaz:
http://arxiv.org/abs/2406.15872
Autor:
Chatterjee, Tapas, Laha, Ayantika
In $1998,$ Daemen {\it{ et al.}} introduced a circulant Maximum Distance Separable (MDS) matrix in the diffusion layer of the Rijndael block cipher, drawing significant attention to circulant MDS matrices. This block cipher is now universally acclaim
Externí odkaz:
http://arxiv.org/abs/2406.14013
Autor:
Chatterjee, Tapas, Laha, Ayantika
In symmetric cryptography, maximum distance separable (MDS) matrices with computationally simple inverses have wide applications. Many block ciphers like AES, SQUARE, SHARK, and hash functions like PHOTON use an MDS matrix in the diffusion layer. In
Externí odkaz:
http://arxiv.org/abs/2406.12842
Autor:
Chatterjee, Tapas, Garg, Sonam
In this article, we aim to extend the research conducted by Chatterjee and Garg in 2024, particularly focusing on the $q$-analogue of the generalized Stieltjes constants. These constants constitute the coefficients in the Laurent series expansion of
Externí odkaz:
http://arxiv.org/abs/2404.09139
Autor:
Chatterjee, Tapas, Garg, Sonam
In this article, our aim is to extend the research conducted by Kurokawa and Wakayama in 2003, particularly focusing on the $q$-analogue of the Hurwitz zeta function. Our specific emphasis lies in exploring the coefficients in the Laurent series expa
Externí odkaz:
http://arxiv.org/abs/2404.08025